Delay Vector Variance (DVV) method, Surrogate Data, Hypothesis Testing, Test Statistics, Signal Nonlinearity and Uncertainty, Wind Modelling


The Delay vector variance (DVV) method uses predictability of the signal in phase space to characterize the time series. Using the surrogate data methodology, so called DVV plots and DVV scatter diagrams can be generated using the DVV method, as a test statistic, to examine the determinism/stochastisity and linearity/nonlinearity within a signal simultaneously. In DVV scatter diagram, the target variance values of the original signal is plotted against the averaged variance values, calculated over a number of iAAFT surrogates. As a result, for linear signals, the scatter diagram coincides with the bisector line and conversely for nonlinear signals, the scatter diagram deviates from bisector lineas shown in the attached document. The DVV method has been successfully applied to analyse the nature of biometric signals (EEG and fMRI).

The DVV Toolbox

A DVV toolbox for MATLAB is provided, which can be downloaded as a zip archive. The code is provided under the GNU General Public License (GPL).

Acknowledgements: Temujin Gautama, Marc Van Hulle, Mo Chen, Naveed Ur Rehman


    Legend: MATLAB code, PDF files, Supplements.

    You can download from here some Wind Data used in some of the simulations in the work below. These are 2D (complex) data, for three different wind regimes of 'low', 'medium', and 'high' dynamics.

  1. T. Gautama, D.P. Mandic, and M. M. Van Hulle, "The delay vector variance method for detecting determinism and nonlinearity in time series," Physica D, vol. 190, no. 3-4, pp. 167-176, 2004. [pdf] [MATLAB code] [Zipped content]
    1. T. Gautama, D.P. Mandic, and M.M. Van Hulle, "Indications of nonlinear structures in brain electrical activity," Phys. Rev. E, vol. 67, 2003. [pdf]
    2. T. Gautama, D.P. Mandic, and M.M. Van Hulle, "A Differential Entropy Based Method for Determining the Optimal Embedding Parameters of a Signal," in Proceedings of ICASSP'03, pp. VI-29 -- VI-32, 2003. [pdf]
    3. T. Gautama, D.P. Mandic, and M.M. Van Hulle, "Signal nonlinearity in fMRI: A comparison between BOLD and MION," IEEE Transactions in Medical Imaging, vol. 22, 2003. [pdf]
    4. D.P. Mandic, M. Chen, T. Gautama, M.M. Van Hulle, and A. Constantinides, "On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series," Proceedings of Royal Society A, vol. 464, pp. 1141-1160, 2008. [pdf]
    5. M. Chen, T. Gautama, and D. P. Mandic, "An assessment of qualitative performance of machine learning architectures: Modular feedback networks," IEEE Transactions on Neural Networks, vol. 19, pp. 183-189, 2008. [pdf]
    6. M. Chen, T. Gautama, M. Griselli, and D. P. Mandic, "Nonlinear Schemes for Heart Valve Failure Detection," in Proceeedings of the 7th IMA International Conference on Mathematics for Signal Processing, pp. 81-84, 2006. [pdf]
    7. D.P. Mandic, M. Golz, A. Kuh, D. Obradovic, and T. Tanaka, Eds., Signal Processing Techniques for Knowledge Extraction and Information Fusion, Springer, 2008. [Amazon]
    8. T. Gautama, D.P. Mandic, and M.M. Van Hulle, "A Novel Method for Determining the Nature of Time Series," IEEE Transactions on Biomedical Engineering, vol. 51, no. 5, pp. 728-736, 2004. [pdf]
    9. T. Gautama, D.P. Mandic, and M.M. Van Hulle, "A non-parametric test for detecting the complex-valued nature of time series," International Journal of Knowledge-Based Intelligent Engineering Systems, vol. 8, no. 2, pp. 99-106, 2004. [pdf]
    10. S. L. Goh, M. Chen, D. H. Popovic, K. Aihara, D. Obradovic and D. P. Mandic, "Complex-Valued Forecasting of Wind Profile," Renewable Energy, vol. 31, pp. 1733-1750, 2006. [pdf]
    11. N. U. Rehman and D. P. Mandic, "Qualitative Analysis of Rotational Modes within Three-Dimensional Empirical Mode Decomposition," in Proceedings of ICASSP 2009, pp. 3449-3452, 2009. [pdf]
    12. D. P. Mandic, P. Vayanos, M. Chen, and S. L. Goh, "Online Detection of the Modality of Complex Valued Real World Signals," International Journal of Neural Systems, vol. 18, no. 2, pp. 67-74, 2008. [pdf]
    13. Y. Yuan, Y. Li, and D. P. Mandic, "Comparison Analysis of Embedding Dimension between Normal and Epileptic EEG Time Series," Journal of Physiological Sciences, vol. 58, no. 4, pp. 239-247, 2008. [pdf]
    14. D.P. Mandic and J. A. Chambers, Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures, and Stability, Wiley, 2001. [Amazon]